Digital Control Strategies With Attractiveness and Invariance Specifications

This paper presents a control design approach for discrete-time input-output systems on the basis of attracting law (AL) with attractiveness and invariance specifications. A measure of disturbance rejection is embedded in the AL, by which a control law is derived. The steady-state error band, absolute attractive layer, and the monotone decreasing region of the error dynamics are defined, and the bounds are derived in detail, in order to characterize the closed-loop performance with respect to control parameter values. It is shown that the chattering can be alleviated by replacing the sign function, involved in the conventional attractive law, with the saturation function. Such an alternative approach is of the equally important feature of the reaching-law approach, namely, the ease of obtaining the control law, the simplicity and efficiency in the implementation, and the resultant robust characteristic to parametric uncertainties and external disturbances. Numerical simulation and experiments are carried out for performance evaluation of the presented control strategies.